As you've already said, the extra capacity should extend your range by approximately 50%.
As far as the power difference is concerned, it will ultimately depend upon the settings of your controller and/or the rating of the battery's cells and
BMS.
If both
BMS units have a higher current rating than the current limit on your motor's controller, it should not make a great deal of difference, except the higher capacity cells are likely to have less voltage sag under the same load
(assuming they have the same quality and type of cells), which will effectively produce slightly more power at the same maximum Amps limit.
However, if the limiting factor of your existing set-up is the
BMS, and the 15Ah battery has a higher current
BMS, you may find that the power will increase quite noticeably.
There is only one way to find out for sure, so let us know the results when you've tested and compared the two batteries on the same bike.
Alan
